Question 838: Electrostatics & Capacitance

Question

Two non-conducting spheres of radii $${R_1}$$ and $${R_2}$$ and carrying uniform volume charge densities $$ + \rho $$ and $$ - \rho ,$$ respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region

Accepted Answer

Here we will use the concept of vectors and concept of electric field.
Let's take a point P in the overlapping region.
From $$\Delta OPQ$$,
By triangle law of vector addition,
$$\overrightarrow {{r_1}}  - \overrightarrow {{r_2}}  = \overrightarrow d \quad 	ext{... (1)}$$
Net electrostatic field at point P;
$${\overrightarrow E _{net}} = {{K{q_1}} \over {r_1^3}}\overrightarrow {{r_1}}  = {{K{q_2}} \over {r_2^3}}\overrightarrow {{r_2}} $$
$$ \Rightarrow {\overrightarrow E _{net}} = {{K\left( {ho {4 \over 3}\pi r_1^3} ight)\overrightarrow {{r_1}} } \over {r_1^3}} - {{K\left( {ho {4 \over 3}\pi r_2^3} ight)\overrightarrow {{r_2}} } \over {r_2^3}}$$
$$ \Rightarrow {\overrightarrow E _{net}} = {4 \over 3}ho \pi  	imes {1 \over {4\pi {\varepsilon _0}}}\left( {\overrightarrow {{r_1}}  - \overrightarrow {{r_2}} } ight)$$
$$ \Rightarrow {\overrightarrow E _{net}} = {ho  \over {3{\varepsilon _0}}}\overrightarrow d $$
Hence, the electrostatic field is constant in magnitude and has same direction.
Therefore, options (C) and (D) are correct.

Answer

The electrostatic field is zero

Answer

The electrostatic potential is constant

Answer

The electrostatic field is constant in magnitude

Answer

The electrostatic field has same direction

Electrostatics & Capacitance

Two non-conducting spheres of radii ${R_1} and {R_2} and carrying uniform volume charge densities + \rho and - \rho ,$ respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region

Choose the correct answer: